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a9d3f29d4f64dd781e2b14eadd416852dc66e53f | 6fbf10071e62af7238f2de8f9aa83d55d8763907 | /examples/and_properties.lean | c7ce193949649ac1116d7ad3896e41aa3611123f | [] | no_license | HasanMukati/uva-cs-dm-s19 | ee5aad4568a3ca330c2738ed579c30e1308b03b0 | 3e7177682acdb56a2d16914e0344c10335583dcf | refs/heads/master | 1,596,946,213,130 | 1,568,221,949,000 | 1,568,221,949,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,675 | lean | namespace and.rassoc
variables P Q R: Prop
#check P ∧ Q ∧ R
#check P ∧ (Q ∧ R)
end and.rassoc
lemma my_and_intro{P Q: Prop}(pfP: P)(pfQ: Q): P ∧ Q :=
begin
exact and.intro pfP pfQ
end
example: ∀{P Q: Prop}(pfPandQ: P ∧ Q),
P :=
begin
intros,
exact pfPandQ.left,
-- can use (and.elim_left pfPandQ) or
... |
f9449318597bcb3631ad62ca006fe4d6e460142c | 6fbf10071e62af7238f2de8f9aa83d55d8763907 | /hw/practice-exam2.lean | 06cc57843d332f98fa4bc514a0617a9284d31c3f | [] | no_license | HasanMukati/uva-cs-dm-s19 | ee5aad4568a3ca330c2738ed579c30e1308b03b0 | 3e7177682acdb56a2d16914e0344c10335583dcf | refs/heads/master | 1,596,946,213,130 | 1,568,221,949,000 | 1,568,221,949,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,108 | lean |
/-
Conjunctions, disjunctions, implication, iff,
negation
-/
/-
1. Prove that 3 + 3 = 6 and 2 + 6 = 8 implies
that 1 + 1 = 2.
-/
-- answer:
/-
2. Prove that 2 + 5 = 3 or 9 + 1 = 5 implies
that 2 + 3 = 9.
-/
-- answer:
/-
3. Prove that ¬(A ∧ B ∧ C) ↔ (¬A ∨ ¬B ∨ ¬C).
You may use the axiom of the excluded middle.
-/... |
de5c43b4199ad346b153b6133cc29320059039c3 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/analysis/special_functions/stirling.lean | fa59c375ca816e22700b184ab5ee42f8ce48451b | [
"Apache-2.0"
] | permissive | jcommelin/mathlib | d8456447c36c176e14d96d9e76f39841f69d2d9b | ee8279351a2e434c2852345c51b728d22af5a156 | refs/heads/master | 1,664,782,136,488 | 1,663,638,983,000 | 1,663,638,983,000 | 132,563,656 | 0 | 0 | Apache-2.0 | 1,663,599,929,000 | 1,525,760,539,000 | Lean | UTF-8 | Lean | false | false | 13,116 | lean | /-
Copyright (c) 2022. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Firsching, Fabian Kruse, Nikolas Kuhn
-/
import analysis.p_series
import analysis.special_functions.log.deriv
import tactic.positivity
import data.real.pi.wallis
/-!
# Stirling's formula
Thi... |
9516913fee4bf45d7e3084b1b54cb19f7fed3c2e | 77c5b91fae1b966ddd1db969ba37b6f0e4901e88 | /src/measure_theory/integral/lebesgue.lean | a50869af26fc2e84b11147075ef4b8442ece14ab | [
"Apache-2.0"
] | permissive | dexmagic/mathlib | ff48eefc56e2412429b31d4fddd41a976eb287ce | 7a5d15a955a92a90e1d398b2281916b9c41270b2 | refs/heads/master | 1,693,481,322,046 | 1,633,360,193,000 | 1,633,360,193,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 107,571 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Johannes Hölzl
-/
import measure_theory.measure.measure_space
import measure_theory.constructions.borel_space
import algebra.indicator_function
import algebra.support
... |
16c74844a91dd41cb4ead62b11c440eeab07f48f | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/algebra/euclidean_absolute_value.lean | 18e8e496bd04c79870662683b53e7083b83d0724 | [
"Apache-2.0"
] | permissive | hikari0108/mathlib | b7ea2b7350497ab1a0b87a09d093ecc025a50dfa | a9e7d333b0cfd45f13a20f7b96b7d52e19fa2901 | refs/heads/master | 1,690,483,608,260 | 1,631,541,580,000 | 1,631,541,580,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,107 | lean | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import algebra.absolute_value
import algebra.euclidean_domain
/-!
# Euclidean absolute values
This file defines a predicate `absolute_value.is_euclidean abv` stating the
... |
74164fd13b075d723b8717d5c27347abfe3d6a78 | ce6917c5bacabee346655160b74a307b4a5ab620 | /src/ch5/ex0718.lean | 3e6f0ccb1b3b899abff012ec781cefb8dc49899f | [] | no_license | Ailrun/Theorem_Proving_in_Lean | ae6a23f3c54d62d401314d6a771e8ff8b4132db2 | 2eb1b5caf93c6a5a555c79e9097cf2ba5a66cf68 | refs/heads/master | 1,609,838,270,467 | 1,586,846,743,000 | 1,586,846,743,000 | 240,967,761 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 519 | lean | import data.list.basic
open list
universe u
variables {α : Type} (x y z : α) (xs ys zs : list α)
def mk_symm (xs : list α) := xs ++ reverse xs
attribute [simp]
theorem reverse_mk_symm (xs : list α) :
reverse (mk_symm xs) = mk_symm xs :=
by simp [mk_symm]
example (xs ys : list ℕ) :
reverse (xs ++ mk_symm ys) = ... |
2e8da3b808b11578d0fbf400ffb20bd072c58c00 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/measure_theory/function/conditional_expectation/basic.lean | 4a716204693171ee959635857767dabc5d0d5102 | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 109,028 | lean | /-
Copyright (c) 2021 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
import analysis.inner_product_space.projection
import measure_theory.function.l2_space
import measure_theory.function.ae_eq_of_integral
/-! # Conditional expectation
W... |
60281e882694301d6b6ee6986a8ad5ef38d00819 | 4b846d8dabdc64e7ea03552bad8f7fa74763fc67 | /library/init/meta/injection_tactic.lean | 33e7be4f1ada0f0d0e2962ad95ba83ef50d48f60 | [
"Apache-2.0"
] | permissive | pacchiano/lean | 9324b33f3ac3b5c5647285160f9f6ea8d0d767dc | fdadada3a970377a6df8afcd629a6f2eab6e84e8 | refs/heads/master | 1,611,357,380,399 | 1,489,870,101,000 | 1,489,870,101,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,745 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.meta.tactic init.function
namespace tactic
open nat tactic environment expr list
private meta def at_end₂ (e₁ e₂ : expr) : ℕ → tactic ... |
1267d79aa981fb5b5c486f3354dd76a459de9700 | a4673261e60b025e2c8c825dfa4ab9108246c32e | /src/Init/Data/Nat/Basic.lean | 46a336452ec7c366b8ab669da17c4c2bdc2259ce | [
"Apache-2.0"
] | permissive | jcommelin/lean4 | c02dec0cc32c4bccab009285475f265f17d73228 | 2909313475588cc20ac0436e55548a4502050d0a | refs/heads/master | 1,674,129,550,893 | 1,606,415,348,000 | 1,606,415,348,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,161 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Leonardo de Moura
-/
prelude
import Init.Core
universes u
namespace Nat
@[specialize] def foldAux {α : Type u} (f : Nat → α → α) (s : Nat) : Nat → α → α
| ... |
eaed6866822464835e8d35f310c66441bde97533 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/run/mk_dec_eq1.lean | 48bdb2049d9d648112afb594044b6013fd95bc01 | [
"Apache-2.0"
] | permissive | soonhokong/lean-osx | 4a954262c780e404c1369d6c06516161d07fcb40 | 3670278342d2f4faa49d95b46d86642d7875b47c | refs/heads/master | 1,611,410,334,552 | 1,474,425,686,000 | 1,474,425,686,000 | 12,043,103 | 5 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 1,014 | lean | open tactic
namespace test
inductive enum1 : Type | ea | eb | ec | ed
attribute [instance]
definition enum1_dec_eq : decidable_eq enum1 :=
by mk_dec_eq_instance
inductive Expr
| var : nat → Expr
| app : ∀ (n : nat) (e1 : Expr) (e2 : Expr) (e3 : Expr) (e4 : Expr), Expr
| Elet : Expr → Expr
| bla : list nat → Exp... |
47885b4e66d2fced2d3b5788aa8aac4a7042b8ec | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/normed_space/extr.lean | 29b2bc70da3a950641e71f3e5e61fbbc51fefc07 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 4,112 | lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import analysis.normed_space.ray
import topology.local_extr
/-!
# (Local) maximums in a normed space
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to t... |
953bbbc373b30e00c870b5a753f99e780a735e9c | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/nat/cast/defs.lean | c459e57ab6c57dd6cb6909a6aab241ecf9b9e5c7 | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 6,484 | lean | /-
Copyright (c) 2014 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Gabriel Ebner
-/
import algebra.group.defs
import algebra.ne_zero
/-!
# Cast of natural numbers
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> https://github.com/leanpr... |
94ce0777d32ce21f0169de03f78204760bcc842f | 9b9a16fa2cb737daee6b2785474678b6fa91d6d4 | /src/group_theory/subgroup.lean | 502540d3936d645af09e1d351a2777e655f49109 | [
"Apache-2.0"
] | permissive | johoelzl/mathlib | 253f46daa30b644d011e8e119025b01ad69735c4 | 592e3c7a2dfbd5826919b4605559d35d4d75938f | refs/heads/master | 1,625,657,216,488 | 1,551,374,946,000 | 1,551,374,946,000 | 98,915,829 | 0 | 0 | Apache-2.0 | 1,522,917,267,000 | 1,501,524,499,000 | Lean | UTF-8 | Lean | false | false | 26,182 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mitchell Rowett, Scott Morrison, Johan Commelin, Mario Carneiro
-/
import group_theory.submonoid
open set function
variables {α : Type*} {β : Type*} {a a₁ a₂ b c: α}
... |
db10edf725ccc28288b40cb4fa478a712c77cfa4 | 77c5b91fae1b966ddd1db969ba37b6f0e4901e88 | /src/data/part.lean | 14a6f46cc34b4ca264aed7e2a860d78231996cc4 | [
"Apache-2.0"
] | permissive | dexmagic/mathlib | ff48eefc56e2412429b31d4fddd41a976eb287ce | 7a5d15a955a92a90e1d398b2281916b9c41270b2 | refs/heads/master | 1,693,481,322,046 | 1,633,360,193,000 | 1,633,360,193,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 16,821 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Jeremy Avigad, Simon Hudon
-/
import data.equiv.basic
/-!
# Partial values of a type
This file defines `part α`, the partial values of a type.
`o : part α` carries a... |
42c5168c9d122aed411d27335c1246c928410ff9 | 69bc7d0780be17e452d542a93f9599488f1c0c8e | /listplayground.lean | 2ba071fcd03b5ea2804eb82db2c61c633ae0f18e | [] | no_license | joek13/cs2102-notes | b7352285b1d1184fae25594f89f5926d74e6d7b4 | 25bb18788641b20af9cf3c429afe1da9b2f5eafb | refs/heads/master | 1,673,461,162,867 | 1,575,561,090,000 | 1,575,561,090,000 | 207,573,549 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,115 | lean | inductive jlist (α : Type) : Type
| nil : jlist
| cons : α → jlist → jlist
open jlist
def nat_list : jlist nat := (cons 1 (cons 2 (cons 3 (nil nat))))
def count {α : Type} : jlist α → nat
| (nil α) := 0
| (cons h t) := 1 + (count t)
#eval count nat_list
def append {α : Type} : jlist α → α → jlist α
| (nil α) e := ... |
05f18724f7848f0b6e78539b3dac8f59fa705ee7 | a721fe7446524f18ba361625fc01033d9c8b7a78 | /src/principia/myring/order.lean | 69008a34524f3503efd3d4f2b56ea00533586a17 | [] | no_license | Sterrs/leaning | 8fd80d1f0a6117a220bb2e57ece639b9a63deadc | 3901cc953694b33adda86cb88ca30ba99594db31 | refs/heads/master | 1,627,023,822,744 | 1,616,515,221,000 | 1,616,515,221,000 | 245,512,190 | 2 | 0 | null | 1,616,429,050,000 | 1,583,527,118,000 | Lean | UTF-8 | Lean | false | false | 23,918 | lean | import .basic
import ..mynat.lt
import ..logic
namespace hidden
class ordered_myring (α : Type) extends myring α, has_le α :=
(decidable_le: ∀ a b: α, decidable (a ≤ b))
(le_add_right {a b} (c : α) : a ≤ b → a + c ≤ b + c)
(zero_le_mul {a b : α} : 0 ≤ a → 0 ≤ b → 0 ≤ a * b)
(le_trans {a} (b : α) {c}: a ≤ b → b ≤ c → ... |
0d81acd07e95675b4d973f425a03fbc27d73f88a | 367134ba5a65885e863bdc4507601606690974c1 | /src/category_theory/limits/pi.lean | 34bd369b5d04c67f5da14c1f62dd47449acd54a0 | [
"Apache-2.0"
] | permissive | kodyvajjha/mathlib | 9bead00e90f68269a313f45f5561766cfd8d5cad | b98af5dd79e13a38d84438b850a2e8858ec21284 | refs/heads/master | 1,624,350,366,310 | 1,615,563,062,000 | 1,615,563,062,000 | 162,666,963 | 0 | 0 | Apache-2.0 | 1,545,367,651,000 | 1,545,367,651,000 | null | UTF-8 | Lean | false | false | 4,501 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.pi.basic
import category_theory.limits.limits
/-!
# Limits in the category of indexed families of objects.
Given a functor `F : J ⥤ Π i, C i`... |
b2e8ed8d186368daff2fba825f524a0cfcd281a0 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/control/equiv_functor/instances.lean | f88b4ca3a9b37bbd84de032ad4b28cb0cde9db1b | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 926 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import data.fintype.basic
import control.equiv_functor
/-!
# `equiv_functor` instances
We derive some `equiv_functor` instances, to enable `equiv_rw` to rewrite und... |
b21725a3019c4a3020d5bc694c3462f6157e6b4b | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /tests/lean/norm_tac.lean | aede4d6190a3792fef438358e5da6ca6073c6442 | [
"Apache-2.0"
] | permissive | codyroux/lean0.1 | 1ce92751d664aacff0529e139083304a7bbc8a71 | 0dc6fb974aa85ed6f305a2f4b10a53a44ee5f0ef | refs/heads/master | 1,610,830,535,062 | 1,402,150,480,000 | 1,402,150,480,000 | 19,588,851 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 460 | lean | import Int
import tactic
set_option pp::implicit true
set_option pp::coercion true
set_option pp::notation false
variable vector (A : Type) (sz : Nat) : Type
variable read {A : Type} {sz : Nat} (v : vector A sz) (i : Nat) (H : i < sz) : A
variable V1 : vector Int 10
axiom H : 1 < 10
add_rewrite H
definition D := read V... |
cb096aae4ceab01fbc674d944669eff880c121d9 | 8b9f17008684d796c8022dab552e42f0cb6fb347 | /hott/init/function.hlean | 803f1aea386bce76ef98a2eaac1d9cb8c1530998 | [
"Apache-2.0"
] | permissive | chubbymaggie/lean | 0d06ae25f9dd396306fb02190e89422ea94afd7b | d2c7b5c31928c98f545b16420d37842c43b4ae9a | refs/heads/master | 1,611,313,622,901 | 1,430,266,839,000 | 1,430,267,083,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,601 | hlean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: init.function
Author: Leonardo de Moura
General operations on functions.
-/
prelude
import init.reserved_notation
namespace function
variables {A : Type} {B : Type} {C : Typ... |
7b7efd7464e8fde9a98860fde2b2b7dacbc383b5 | 3dc4623269159d02a444fe898d33e8c7e7e9461b | /.github/workflows/project_1_a_decrire/foncteur/comax.lean | b1ec5cf50c3be4944da20e48043b7c2563ae8449 | [] | no_license | Or7ando/lean | cc003e6c41048eae7c34aa6bada51c9e9add9e66 | d41169cf4e416a0d42092fb6bdc14131cee9dd15 | refs/heads/master | 1,650,600,589,722 | 1,587,262,906,000 | 1,587,262,906,000 | 255,387,160 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,795 | lean | import tactic.ring
import tactic.ring_exp
import algebra.category.CommRing.basic
open CommRing
universes v u
local notation ` Ring ` := CommRing.{u}
local notation ` Set ` := Type u
--- Study of co-maximal familly ! I do the job why two elements for the moment !
--- This is good... |
0d099a5b367c706060bce49b9095718988f0293a | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/abstract_ns.lean | 6889a9be1e8ce96a718464eb30cbcb1374103036 | [
"Apache-2.0"
] | permissive | leanprover-community/lean | 12b87f69d92e614daea8bcc9d4de9a9ace089d0e | cce7990ea86a78bdb383e38ed7f9b5ba93c60ce0 | refs/heads/master | 1,687,508,156,644 | 1,684,951,104,000 | 1,684,951,104,000 | 169,960,991 | 457 | 107 | Apache-2.0 | 1,686,744,372,000 | 1,549,790,268,000 | C++ | UTF-8 | Lean | false | false | 202 | lean | -- Each abstract_ns[i] module contains a definition ns[i].foo with an abstracted nested proof.
-- This test makes sure that the abstracted proofs get different names.
import .abstract_ns1 .abstract_ns2
|
e8adadea79f037961596080f190d5490c89b3501 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/group_theory/subsemigroup/centralizer.lean | 21398b2b814219fa628cf35fe0900b6ccaea9c20 | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 4,928 | lean | /-
Copyright (c) 2021 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning, Jireh Loreaux
-/
import group_theory.subsemigroup.center
import algebra.group_with_zero.units.lemmas
/-!
# Centralizers of magmas and semigroups
## Main definitions... |
7021b79040d04ab91e6d2d3c2ab8c8512a6be496 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/analysis/normed_space/real_inner_product.lean | 5523a13fbd02a6cbc56fbadef2b49b06fa33b23d | [
"Apache-2.0"
] | permissive | gebner/mathlib | eab0150cc4f79ec45d2016a8c21750244a2e7ff0 | cc6a6edc397c55118df62831e23bfbd6e6c6b4ab | refs/heads/master | 1,625,574,853,976 | 1,586,712,827,000 | 1,586,712,827,000 | 99,101,412 | 1 | 0 | Apache-2.0 | 1,586,716,389,000 | 1,501,667,958,000 | Lean | UTF-8 | Lean | false | false | 22,078 | lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou
-/
import analysis.convex.basic algebra.quadratic_discriminant analysis.complex.exponential
analysis.specific_limits
import tactic.monotonicity
/-!
# Inner Produ... |
9707b05f7ad72c3f21cb53e03276ae98353b92ea | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /tests/lean/run/refine3.lean | 1b64b6e8fa199a1237b29628694fb32db000061e | [
"Apache-2.0"
] | permissive | davidmueller13/lean | 65a3ed141b4088cd0a268e4de80eb6778b21a0e9 | c626e2e3c6f3771e07c32e82ee5b9e030de5b050 | refs/heads/master | 1,611,278,313,401 | 1,444,021,177,000 | 1,444,021,177,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 269 | lean | import data.nat.basic
open nat
theorem zero_left (n : ℕ) : 0 + n = n :=
nat.induction_on n
!add_zero
(take m IH,
begin
refine
(calc
0 + succ m = succ (0 + m) : _
... = succ m : IH),
esimp
end)
|
fd7faf982932a7403f47786fb19ba92db65cbfa5 | 6e36ebd5594a0d512dea8bc6ffe78c71b5b5032d | /src/mywork/Practice/practice_2.lean | 64c4d69cdd8b95829bcaace1387100773e054ab9 | [] | no_license | wrw2ztk/cs2120f21 | cdc4b1b4043c8ae8f3c8c3c0e91cdacb2cfddb16 | f55df4c723d3ce989908679f5653e4be669334ae | refs/heads/main | 1,691,764,473,342 | 1,633,707,809,000 | 1,633,707,809,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,748 | lean | /-
Wyndham White (working alone)
wrw2ztk
https://github.com/wyndhamv/cs2120f21.git
-/
/-
Prove the following simple logical conjectures.
Give a formal and an English proof of each one.
Your English language proofs should be complete
in the sense that they identify all the axioms
and/or theorems that you use.
-/
examp... |
60daa59c8367754316f1b22f9f2ffc984e769cba | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/measure_theory/integral/bochner.lean | 77a7394ccaa225f9e04bdbe834dbb0c1de3be2d9 | [
"Apache-2.0"
] | permissive | robertylewis/mathlib | 3d16e3e6daf5ddde182473e03a1b601d2810952c | 1d13f5b932f5e40a8308e3840f96fc882fae01f0 | refs/heads/master | 1,651,379,945,369 | 1,644,276,960,000 | 1,644,276,960,000 | 98,875,504 | 0 | 0 | Apache-2.0 | 1,644,253,514,000 | 1,501,495,700,000 | Lean | UTF-8 | Lean | false | false | 66,642 | lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Yury Kudryashov, Sébastien Gouëzel, Rémy Degenne
-/
import measure_theory.integral.set_to_l1
import measure_theory.group.basic
import analysis.normed_space.bounded_linear... |
adef526673b288920e89c607ee56a78a2fe58a4f | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/category_theory/adjunction/opposites.lean | 99c9fc73f1426f4dc270c5756c781c972856fe9c | [
"Apache-2.0"
] | permissive | robertylewis/mathlib | 3d16e3e6daf5ddde182473e03a1b601d2810952c | 1d13f5b932f5e40a8308e3840f96fc882fae01f0 | refs/heads/master | 1,651,379,945,369 | 1,644,276,960,000 | 1,644,276,960,000 | 98,875,504 | 0 | 0 | Apache-2.0 | 1,644,253,514,000 | 1,501,495,700,000 | Lean | UTF-8 | Lean | false | false | 10,740 | lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Thomas Read, Andrew Yang
-/
import category_theory.adjunction.basic
import category_theory.yoneda
import category_theory.opposites
/-!
# Opposite adjunctions
This file c... |
8617d16923f44f1eb9a9298164dfde3d5b5389a5 | 137d14933f47decc2ad59a16298d2e371f4ac8c1 | /examples/src/sandwich.lean | 77cdc2fb98abbe3ad7a381f8085e07582f7a5092 | [
"Apache-2.0"
] | permissive | leanprover-community/format_lean | 08af277ef0c1366e095b9d8d1e29dbae81612984 | b8a1eff6922b78185596c4500504fa7edd9b2242 | refs/heads/master | 1,677,151,038,043 | 1,675,429,968,000 | 1,675,429,968,000 | 169,313,562 | 65 | 14 | Apache-2.0 | 1,593,167,360,000 | 1,549,401,112,000 | Python | UTF-8 | Lean | false | false | 2,356 | lean | -- begin header
-- Everything in the header will be hidden in the HTML file.
import data.real.basic
notation `|` x `|` := abs x
@[user_attribute]
meta def ineq_rules : user_attribute :=
{ name := `ineq_rules,
descr := "lemmas usable to prove inequalities" }
attribute [ineq_rules] add_lt_add le_max_left le_max_rig... |
8969fe6ab3a73a81f3f136e5271f260139d3fb38 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/algebra/continued_fractions/computation/correctness_terminating.lean | 7f764df0621efce8a00f8a9a1d8b7af4ec409fb3 | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 12,351 | lean | /-
Copyright (c) 2020 Kevin Kappelmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann
-/
import algebra.continued_fractions.computation.translations
import algebra.continued_fractions.terminated_stable
import algebra.continued_fractions.continuants_re... |
87ef7531998be36caac517af9a931d5547199e7d | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /test/hint.lean | 5b401d080384aee045751b0a30ae4ebacdfdbd35 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 1,304 | lean | import tactic.hint
import tactic.split_ifs
import tactic.finish
example : 1 = 1 :=
begin
(do hints ← tactic.hint, guard $ ("refl", 0) ∈ hints),
refl
end
-- `split_ifs` is designated as a `hint_tactic` in its own file
example : if 1 = 1 then true else false :=
begin
(do hints ← tactic.hint, guard $ ("split_ifs",... |
c282c65328872dfda7c3bb898bc1ef49a18b73a7 | ac2987d8c7832fb4a87edb6bee26141facbb6fa0 | /Mathlib/Logic/Basic.lean | a80ab5c3da71ef57bcb5b01e9dc69d875f2e652a | [
"Apache-2.0"
] | permissive | AurelienSaue/mathlib4 | 52204b9bd9d207c922fe0cf3397166728bb6c2e2 | 84271fe0875bafdaa88ac41f1b5a7c18151bd0d5 | refs/heads/master | 1,689,156,096,545 | 1,629,378,840,000 | 1,629,378,840,000 | 389,648,603 | 0 | 0 | Apache-2.0 | 1,627,307,284,000 | 1,627,307,284,000 | null | UTF-8 | Lean | false | false | 28,946 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura
-/
import Mathlib.Init.Logic
import Mathlib.Function
import Mathlib.Tactic.Basic
section needs_better_home
/- This section contains items that have no ... |
4c1bfd7b2f8e325d80ab2cc747f986600469132b | 79627aa58926a60af8625f63439c85235eeba719 | /src/data/mv_polynomial.lean | 53f59c02a4b78655e54d6487b321db9fff417830 | [
"Apache-2.0"
] | permissive | fgdorais/mathlib | 5cfee4f41a23c6ca57f6880210461dd146a555df | 8eaf478a8d96bce3c62573ae452f86672aea4d66 | refs/heads/master | 1,598,623,421,152 | 1,572,094,703,000 | 1,572,094,703,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 44,201 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro
Multivariate Polynomial
-/
import algebra.ring
import data.finsupp data.polynomial data.equiv.algebra
noncomputable theory
local attrib... |
c9f8189fcc2a38da09042d5bb23ddd8d4c28e2a3 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/group_theory/free_group.lean | d11aac40bc13a4b4a9ae52c3fb753a1fdc47261e | [
"Apache-2.0"
] | permissive | urkud/mathlib | eab80095e1b9f1513bfb7f25b4fa82fa4fd02989 | 6379d39e6b5b279df9715f8011369a301b634e41 | refs/heads/master | 1,658,425,342,662 | 1,658,078,703,000 | 1,658,078,703,000 | 186,910,338 | 0 | 0 | Apache-2.0 | 1,568,512,083,000 | 1,557,958,709,000 | Lean | UTF-8 | Lean | false | false | 32,645 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import data.fintype.basic
import group_theory.subgroup.basic
/-!
# Free groups
This file defines free groups over a type. Furthermore, it is shown that the free group constru... |
7787c5e3cbbd93fba9bb986a34d50135884f0e7e | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/group_theory/divisible.lean | 63185f2f54c8f2dd8cf8966d088851130a312666 | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 10,498 | lean | /-
Copyright (c) 2022 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
import group_theory.subgroup.pointwise
import group_theory.quotient_group
import algebra.group.pi
/-!
# Divisible Group and rootable group
In this file, we define a div... |
715a7551b5b4642eea55e58304a89ceb48cc8360 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/topology/connected.lean | 6c1bde7257c5a604308770a5fceda48cd7f93194 | [
"Apache-2.0"
] | permissive | ramonfmir/mathlib | c5dc8b33155473fab97c38bd3aa6723dc289beaa | 14c52e990c17f5a00c0cc9e09847af16fabbed25 | refs/heads/master | 1,661,979,343,526 | 1,660,830,384,000 | 1,660,830,384,000 | 182,072,989 | 0 | 0 | null | 1,555,585,876,000 | 1,555,585,876,000 | null | UTF-8 | Lean | false | false | 71,361 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Yury Kudryashov
-/
import data.int.succ_pred
import data.nat.succ_pred
import order.partial_sups
import order.succ_pred.relation
import topology.subset_... |
3413aefd96e359f9e938fc00e26bb275f0219de3 | 130c49f47783503e462c16b2eff31933442be6ff | /tests/playground/matchEqs.lean | 841da3ba2dae4e9fb13bb060672fbf759ba4cee3 | [
"Apache-2.0"
] | permissive | Hazel-Brown/lean4 | 8aa5860e282435ffc30dcdfccd34006c59d1d39c | 79e6732fc6bbf5af831b76f310f9c488d44e7a16 | refs/heads/master | 1,689,218,208,951 | 1,629,736,869,000 | 1,629,736,896,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,285 | lean | import Lean
syntax (name := test) "test%" ident : command
open Lean.Elab
open Lean.Elab.Command
@[commandElab test] def elabTest : CommandElab := fun stx => do
let id ← resolveGlobalConstNoOverloadWithInfo stx[1]
liftTermElabM none do
Lean.Meta.Match.mkEquationsFor id
return ()
def f (xs ys : List String) ... |
e47e62f1e3a91f8022e914721e8d258aafe26895 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /hott/cubical/square.hlean | 99635fe454facedfd8cc85bf631be3931e91969e | [
"Apache-2.0"
] | permissive | soonhokong/lean-osx | 4a954262c780e404c1369d6c06516161d07fcb40 | 3670278342d2f4faa49d95b46d86642d7875b47c | refs/heads/master | 1,611,410,334,552 | 1,474,425,686,000 | 1,474,425,686,000 | 12,043,103 | 5 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 27,626 | hlean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Jakob von Raumer
Squares in a type
-/
import types.eq
open eq equiv is_equiv sigma
namespace eq
variables {A B : Type} {a a' a'' a₀₀ a₂₀ a₄₀ a₀₂ a₂₂ a₂₄ a₀₄ a₄... |
9b7deed5c3941d92c40e790d4c172634ce74c753 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/padics/hensel_auto.lean | 5394fd10e4df0645c9aee86469a41aafd4b678bf | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,038 | lean | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.padics.padic_integers
import Mathlib.topology.metric_space.cau_seq_filter
import Mat... |
09e27086f6145d27b8284765e476dd8871de0244 | a7dd8b83f933e72c40845fd168dde330f050b1c9 | /src/category_theory/instances/TopCommRing/basic.lean | 8c89b62fdf3fe4b861e6839310b77deced8d007a | [
"Apache-2.0"
] | permissive | NeilStrickland/mathlib | 10420e92ee5cb7aba1163c9a01dea2f04652ed67 | 3efbd6f6dff0fb9b0946849b43b39948560a1ffe | refs/heads/master | 1,589,043,046,346 | 1,558,938,706,000 | 1,558,938,706,000 | 181,285,984 | 0 | 0 | Apache-2.0 | 1,568,941,848,000 | 1,555,233,833,000 | Lean | UTF-8 | Lean | false | false | 3,067 | lean | import category_theory.instances.CommRing.basic
import category_theory.instances.Top.basic
import topology.instances.complex
universes u
open category_theory
namespace category_theory.instances
structure TopCommRing :=
(α : Type u)
[is_comm_ring : comm_ring α]
[is_topological_space : topological_space α]
[is_topolo... |
a8eadaca04edd27ef460da1d42ff87d0d088d6ec | 8b147c3d61a55005ca839480a4045e69683f7655 | /connect.lean | 00ccc32ee6a0b7915ed70680cc99d1425e528530 | [] | no_license | dselsam/unrealistic_compiler | ce69efac0d573642b67f44a63eb5f18cdf596b27 | 70514de492a6a1ed705ad247333ae5b3f8455a83 | refs/heads/master | 1,609,483,664,302 | 1,500,654,169,000 | 1,500,654,169,000 | 97,516,326 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 62 | lean | import data.hash_map .atom .nominal_machine .locally_nameless
|
b56322b1360eea276127fe87fe249afdbe1e6739 | 618003631150032a5676f229d13a079ac875ff77 | /src/data/set/intervals/unordered_interval.lean | f6dfd4ce9cf3e8b419fee33fa225b549e94158aa | [
"Apache-2.0"
] | permissive | awainverse/mathlib | 939b68c8486df66cfda64d327ad3d9165248c777 | ea76bd8f3ca0a8bf0a166a06a475b10663dec44a | refs/heads/master | 1,659,592,962,036 | 1,590,987,592,000 | 1,590,987,592,000 | 268,436,019 | 1 | 0 | Apache-2.0 | 1,590,990,500,000 | 1,590,990,500,000 | null | UTF-8 | Lean | false | false | 5,090 | lean | /-
Copyright (c) 2020 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou
-/
import order.bounds
/-!
# Intervals without endpoints ordering
In any decidable linear order `α`, we define the set of elements lying between two elements `a` and
`b`... |
455ed5ff13655a684c36f4da1bc3ac1d300bdf3a | 4fa161becb8ce7378a709f5992a594764699e268 | /src/data/set/intervals/basic.lean | e647aa0f53818a07f1787bae3c226b4aabc6ae85 | [
"Apache-2.0"
] | permissive | laughinggas/mathlib | e4aa4565ae34e46e834434284cb26bd9d67bc373 | 86dcd5cda7a5017c8b3c8876c89a510a19d49aad | refs/heads/master | 1,669,496,232,688 | 1,592,831,995,000 | 1,592,831,995,000 | 274,155,979 | 0 | 0 | Apache-2.0 | 1,592,835,190,000 | 1,592,835,189,000 | null | UTF-8 | Lean | false | false | 28,303 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot, Yury Kudryashov
-/
import tactic.tauto
import algebra.order_functions
import algebra.ordered_field
/-!
# Intervals
In any preorder `α`... |
aabfa99a22d4867b76eff4ba9c09afee696e23f2 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/data/nat/totient.lean | 5fd59e13f2c9935fdad2d23236ff7ef84a6a172f | [
"Apache-2.0"
] | permissive | AntoineChambert-Loir/mathlib | 64aabb896129885f12296a799818061bc90da1ff | 07be904260ab6e36a5769680b6012f03a4727134 | refs/heads/master | 1,693,187,631,771 | 1,636,719,886,000 | 1,636,719,886,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,754 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import algebra.big_operators.basic
import data.nat.prime
import data.zmod.basic
/-!
# Euler's totient function
This file defines [Euler's totient function](https://en.w... |
7ab612cc342ac31291bf949b2cce70c8dccf5bff | e9dbaaae490bc072444e3021634bf73664003760 | /src/Problems/2007/IMO_2007_P4.lean | 642aa9c61323e95a6d2cf83250cf66fe640c4a48 | [
"Apache-2.0"
] | permissive | liaofei1128/geometry | 566d8bfe095ce0c0113d36df90635306c60e975b | 3dd128e4eec8008764bb94e18b932f9ffd66e6b3 | refs/heads/master | 1,678,996,510,399 | 1,581,454,543,000 | 1,583,337,839,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 447 | lean | import Geo.Geo.Core
namespace Geo
open Angle Triangle
def IMO_2007_P4 : Prop :=
∀ (A B C P Q R : Point),
intersectAt₂ (bisector ⟨B, C, A⟩) (Triangle.circumcircle ⟨A, B, C⟩) C R →
intersectAt (bisector ⟨B, C, A⟩) (perpBis (Seg.mk B C)) P →
intersectAt (bisector ⟨B, C, A⟩) (perpBis (Seg.mk A C)) Q →
let K := (Seg.mk B... |
b70465b5b28d83028169e77f1baf4393416f7092 | 4b846d8dabdc64e7ea03552bad8f7fa74763fc67 | /library/data/hash_map.lean | 3d86d6e449dda9fd22000ad1e6746a1864d4fbf5 | [
"Apache-2.0"
] | permissive | pacchiano/lean | 9324b33f3ac3b5c5647285160f9f6ea8d0d767dc | fdadada3a970377a6df8afcd629a6f2eab6e84e8 | refs/heads/master | 1,611,357,380,399 | 1,489,870,101,000 | 1,489,870,101,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,614 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
universes u v w
def bucket_array (α : Type u) (β : α → Type v) (n : nat) :=
array (list (Σ a, β a)) n
structure hash_map (α : Type u) [decidable_eq α] (β :... |
3d739cf11831ba8814b7991e14b524793a3b9594 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/ring_theory/int/basic.lean | b457c9adad45093634f40fda6b25ffc5f26a2135 | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 14,494 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jens Wagemaker, Aaron Anderson
-/
import algebra.euclidean_domain.basic
import data.nat.prime
import ring_theory.coprime.basic
import ring_theory.principal_ideal_domain... |
7ed79e8355640b946b8c7f831f7900685c58ae1d | 94e33a31faa76775069b071adea97e86e218a8ee | /src/analysis/normed_space/lp_space.lean | 0c9e4bb7875ade1dfb770cdef18de050f4fa9a03 | [
"Apache-2.0"
] | permissive | urkud/mathlib | eab80095e1b9f1513bfb7f25b4fa82fa4fd02989 | 6379d39e6b5b279df9715f8011369a301b634e41 | refs/heads/master | 1,658,425,342,662 | 1,658,078,703,000 | 1,658,078,703,000 | 186,910,338 | 0 | 0 | Apache-2.0 | 1,568,512,083,000 | 1,557,958,709,000 | Lean | UTF-8 | Lean | false | false | 39,981 | lean | /-
Copyright (c) 2021 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
import analysis.mean_inequalities
import analysis.mean_inequalities_pow
import analysis.normed.group.pointwise
import topology.algebra.order.liminf_limsup
/-!
# ℓp... |
414f2f425bfc6ec0744ed2ae3e63f9eb10fe5ac4 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/number_theory/padics/padic_integers.lean | d2355532952878461eca799229679ce988c61624 | [
"Apache-2.0"
] | permissive | robertylewis/mathlib | 3d16e3e6daf5ddde182473e03a1b601d2810952c | 1d13f5b932f5e40a8308e3840f96fc882fae01f0 | refs/heads/master | 1,651,379,945,369 | 1,644,276,960,000 | 1,644,276,960,000 | 98,875,504 | 0 | 0 | Apache-2.0 | 1,644,253,514,000 | 1,501,495,700,000 | Lean | UTF-8 | Lean | false | false | 20,818 | lean | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Mario Carneiro, Johan Commelin
-/
import data.int.modeq
import number_theory.padics.padic_numbers
import ring_theory.discrete_valuation_ring
import topology.metric_sp... |
dbde33e678d79a5e2b70a2904589b4e9908e9a31 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/linear_algebra/quadratic_form/basic.lean | 3e8bb33429bcdf6eb63649e8ea5bb2f031dcfe05 | [
"Apache-2.0"
] | permissive | waynemunro/mathlib | e3fd4ff49f4cb43d4a8ded59d17be407bc5ee552 | 065a70810b5480d584033f7bbf8e0409480c2118 | refs/heads/master | 1,693,417,182,397 | 1,634,644,781,000 | 1,634,644,781,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 36,601 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Kexing Ying, Eric Wieser
-/
import algebra.invertible
import linear_algebra.bilinear_form
import linear_algebra.matrix.determinant
import linear_algebra.special_linear_group... |
8f5573c56f01a5b0d7c89d93668c142ed10eb2df | 4727251e0cd73359b15b664c3170e5d754078599 | /src/combinatorics/quiver/arborescence.lean | 8bf4a0e6207f1922ab0f4f4de68f44f0dca6004c | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 4,877 | lean | /-
Copyright (c) 2021 David Wärn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn
-/
import order.well_founded
import data.nat.basic
import combinatorics.quiver.subquiver
import combinatorics.quiver.path
/-!
# Arborescences
A quiver `V` is an arborescence (... |
f0c550f91aed681e39df0a7daaf0eaf8eecbcb1b | 26ac254ecb57ffcb886ff709cf018390161a9225 | /src/topology/homeomorph.lean | bd82540507f0a4c25e814f09e85111c97582f5a9 | [
"Apache-2.0"
] | permissive | eric-wieser/mathlib | 42842584f584359bbe1fc8b88b3ff937c8acd72d | d0df6b81cd0920ad569158c06a3fd5abb9e63301 | refs/heads/master | 1,669,546,404,255 | 1,595,254,668,000 | 1,595,254,668,000 | 281,173,504 | 0 | 0 | Apache-2.0 | 1,595,263,582,000 | 1,595,263,581,000 | null | UTF-8 | Lean | false | false | 8,904 | lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Sébastien Gouëzel, Zhouhang Zhou, Reid Barton
-/
import topology.dense_embedding
open set
variables {α : Type*} {β : Type*} {γ : Type*} {δ : Type*}
/-- ... |
c5cb7f73eed31a590c0e3d6b4809f5fc4993a6e6 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/data/fintype/basic.lean | d2ec81108d3d6322b69bfd440eaa1e43c3b7cbfc | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 67,322 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
Finite types.
-/
import tactic.wlog
import data.finset.powerset
import data.finset.lattice
import data.finset.pi
import data.array.lemmas
import order.well_founded
impo... |
ec296528a888c32d63e459281402886adc678784 | d531288a798ba153485c54976a6d77d1c10fed24 | /src/deletion.lean | 886ba91b7ff40ad3d864d6237cdee14db05c3b1a | [] | no_license | EdAyers/lean-humanproof | f757f6d40bd57ce44f5e92f89b1c1994afb0ad05 | 7fa4cc5a95c1bd4d7dc309bb8c132a6ca500fe8e | refs/heads/master | 1,585,168,875,076 | 1,533,927,266,000 | 1,533,927,266,000 | 144,141,041 | 5 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,357 | lean |
-- deletion tactics for G&G prover
import meta.expr
open tactic expr
universes u v w
def list.mchoose {m : Type u → Type v} [monad m] {α : Type w} {β : Type u} (f : α → m (option β)) : list α → m (list β)
| [] := return []
| (h :: t) := pure (λ (h : option β) (t : list β), option.rec_on h t (λ h, h :: t)) <*> ... |
015fe6e37c8c089414e8e4c6ffa494bc2c602d31 | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/computability/primrec.lean | 483f414983bd363923aa6797318b4a2511c47143 | [
"Apache-2.0"
] | permissive | agjftucker/mathlib | d634cd0d5256b6325e3c55bb7fb2403548371707 | 87fe50de17b00af533f72a102d0adefe4a2285e8 | refs/heads/master | 1,625,378,131,941 | 1,599,166,526,000 | 1,599,166,526,000 | 160,748,509 | 0 | 0 | Apache-2.0 | 1,544,141,789,000 | 1,544,141,789,000 | null | UTF-8 | Lean | false | false | 52,068 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
-/
import data.equiv.list
import logic.function.iterate
/-!
# The primitive recursive functions
The primitive recursive functions are the least collection of functions
... |
a0b291661cc77922c5b20f5db32d4a2d6713607c | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /src/Init/Data/Basic.lean | e849e784b17136b07627e910d4010d2fc95f6bfd | [
"Apache-2.0"
] | permissive | mhuisi/lean4 | 28d35a4febc2e251c7f05492e13f3b05d6f9b7af | dda44bc47f3e5d024508060dac2bcb59fd12e4c0 | refs/heads/master | 1,621,225,489,283 | 1,585,142,689,000 | 1,585,142,689,000 | 250,590,438 | 0 | 2 | Apache-2.0 | 1,602,443,220,000 | 1,585,327,814,000 | C | UTF-8 | Lean | false | false | 442 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import Init.Data.Nat.Basic
import Init.Data.Fin.Basic
import Init.Data.List.Basic
import Init.Data.Char.Basic
import Init.Data.String.Basic
import I... |
dd2c61aeb97da7247209cecccb943a8bd4695a81 | 5ee26964f602030578ef0159d46145dd2e357ba5 | /src/adic_space.lean | dfa1982b8b8dbbcf56b757ed5b76443fa5d78273 | [
"Apache-2.0"
] | permissive | fpvandoorn/lean-perfectoid-spaces | 569b4006fdfe491ca8b58dd817bb56138ada761f | 06cec51438b168837fc6e9268945735037fd1db6 | refs/heads/master | 1,590,154,571,918 | 1,557,685,392,000 | 1,557,685,392,000 | 186,363,547 | 0 | 0 | Apache-2.0 | 1,557,730,933,000 | 1,557,730,933,000 | null | UTF-8 | Lean | false | false | 18,559 | lean | import data.nat.prime
import algebra.group_power
import topology.algebra.ring
import topology.opens
import category_theory.category
import category_theory.full_subcategory
import for_mathlib.prime
import for_mathlib.sheaves.sheaf_of_topological_rings
import for_mathlib.opens
import for_mathlib.open_embeddings
import ... |
6c48e4ab73bd2c1bd11186e97d9bc00b574b128f | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/algebra/homology/image_to_kernel_map.lean | aa9ccb4e17696ee087a2cd9ec31deb9cf119b331 | [
"Apache-2.0"
] | permissive | ilitzroth/mathlib | ea647e67f1fdfd19a0f7bdc5504e8acec6180011 | 5254ef14e3465f6504306132fe3ba9cec9ffff16 | refs/heads/master | 1,680,086,661,182 | 1,617,715,647,000 | 1,617,715,647,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,679 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.limits.shapes.images
import category_theory.limits.shapes.kernels
/-!
# The morphism from `image f` to `kernel g` when `f ≫ g = 0`
We define ... |
d147dfcb74d4103b14d40acf85447ece89c7858c | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/limits/preserves/shapes/products.lean | 8d27b0f9ad99a7da6c2c2c57955b44f6bdbac2cb | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,018 | lean | /-
Copyright (c) 2020 Scott Morrison, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Bhavik Mehta
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.category_theory.limits.shapes.products
import Mathlib.category_... |
9b9c8bb18aad326c7fd24fb8c14934acc2234925 | 367134ba5a65885e863bdc4507601606690974c1 | /src/tactic/fin_cases.lean | 226a5a64a3a1126c1a2323b306839ddbc331ab5c | [
"Apache-2.0"
] | permissive | kodyvajjha/mathlib | 9bead00e90f68269a313f45f5561766cfd8d5cad | b98af5dd79e13a38d84438b850a2e8858ec21284 | refs/heads/master | 1,624,350,366,310 | 1,615,563,062,000 | 1,615,563,062,000 | 162,666,963 | 0 | 0 | Apache-2.0 | 1,545,367,651,000 | 1,545,367,651,000 | null | UTF-8 | Lean | false | false | 4,875 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Scott Morrison
Case bashing:
* on `x ∈ A`, for `A : finset α` or `A : list α`, or
* on `x : A`, with `[fintype A]`.
-/
import data.fintype.basic
import tactic.norm_num
namespace tacti... |
3380cc01bb3e48741f6855e39d4cac8c073d08c2 | 137c667471a40116a7afd7261f030b30180468c2 | /src/algebra/ordered_group.lean | eaa1a801e7bae0bf246a15746a1e995cee9a569f | [
"Apache-2.0"
] | permissive | bragadeesh153/mathlib | 46bf814cfb1eecb34b5d1549b9117dc60f657792 | b577bb2cd1f96eb47031878256856020b76f73cd | refs/heads/master | 1,687,435,188,334 | 1,626,384,207,000 | 1,626,384,207,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 44,470 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Mario Carneiro, Johannes Hölzl
-/
import algebra.ordered_monoid
import order.rel_iso
/-!
# Ordered groups
This file develops the basics of ordered gr... |
3567a5b480730ee12ead9ae75fc33fe614a0c0fb | 1fd908b06e3f9c1252cb2285ada1102623a67f72 | /init/logic.lean | cd5cbe3491864a52c94258565e4a23bd7b82d23f | [
"Apache-2.0"
] | permissive | avigad/hott3 | 609a002849182721e7c7ae536d9f1e2956d6d4d3 | f64750cd2de7a81e87d4828246d1369d59f16f43 | refs/heads/master | 1,629,027,243,322 | 1,510,946,717,000 | 1,510,946,717,000 | 103,570,461 | 0 | 0 | null | 1,505,415,620,000 | 1,505,415,620,000 | null | UTF-8 | Lean | false | false | 21,360 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Floris van Doorn
-/
import .path .meta.rewrite
universes u v w
hott_theory
/- prod -/
@[reducible] def pair := @prod.mk
@[hott] protected def prod.elim {a... |
d860d2d4e0eb55fe13327ec6da9ae8ef917ca196 | bb31430994044506fa42fd667e2d556327e18dfe | /src/data/finset/sigma.lean | 6c463ce72a0fb8d4b4e46dfabedf1dc59a35b2ee | [
"Apache-2.0"
] | permissive | sgouezel/mathlib | 0cb4e5335a2ba189fa7af96d83a377f83270e503 | 00638177efd1b2534fc5269363ebf42a7871df9a | refs/heads/master | 1,674,527,483,042 | 1,673,665,568,000 | 1,673,665,568,000 | 119,598,202 | 0 | 0 | null | 1,517,348,647,000 | 1,517,348,646,000 | null | UTF-8 | Lean | false | false | 6,296 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Yaël Dillies, Bhavik Mehta
-/
import data.finset.lattice
import data.set.sigma
/-!
# Finite sets in a sigma type
This file defines a few `finset` constructions on `Σ ... |
cad1e8afbfd6c7238d6bf6b715def6782ec6ed69 | 690889011852559ee5ac4dfea77092de8c832e7e | /src/analysis/normed_space/operator_norm.lean | 9288046b9fe25e9deebe152af4f05b57cc7c2a8f | [
"Apache-2.0"
] | permissive | williamdemeo/mathlib | f6df180148f8acc91de9ba5e558976ab40a872c7 | 1fa03c29f9f273203bbffb79d10d31f696b3d317 | refs/heads/master | 1,584,785,260,929 | 1,572,195,914,000 | 1,572,195,913,000 | 138,435,193 | 0 | 0 | Apache-2.0 | 1,529,789,739,000 | 1,529,789,739,000 | null | UTF-8 | Lean | false | false | 10,799 | lean | /-
Copyright (c) 2019 Jan-David Salchow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo
Operator norm on the space of continuous linear maps
Define the operator norm on the space of continuous linear maps between normed s... |
ae09af97a8dafdc5239b72ffcafefe50a7ed7d42 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/model_theory/encoding.lean | 6b7c3527220d9af9d661cdc71636934fbba6ad79 | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 14,174 | lean | /-
Copyright (c) 2022 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import computability.encoding
import logic.small.list
import model_theory.syntax
import set_theory.cardinal.ordinal
/-! # Encodings and Cardinality of First-Order S... |
83ef1a44343d05716ad04a25dee9431402b9e790 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/topology/instances/real_vector_space.lean | baa8d723b86b6e6cc19406569c0ea4f90ab316fd | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 2,442 | lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import topology.algebra.module.basic
import topology.instances.real
import topology.instances.rat
/-!
# Continuous additive maps are `ℝ`-linear
In this file we pr... |
6a5126a1df1aa357e6819b5a9ba262badc35fcc2 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/complete_rec_var.lean | 04eeb7cec2abca9f86eaec226d69c3af786662c4 | [
"Apache-2.0"
] | permissive | leanprover-community/lean | 12b87f69d92e614daea8bcc9d4de9a9ace089d0e | cce7990ea86a78bdb383e38ed7f9b5ba93c60ce0 | refs/heads/master | 1,687,508,156,644 | 1,684,951,104,000 | 1,684,951,104,000 | 169,960,991 | 457 | 107 | Apache-2.0 | 1,686,744,372,000 | 1,549,790,268,000 | C++ | UTF-8 | Lean | false | false | 244 | lean | def f : nat → nat → nat
| (x+1) (y+1) := f (x+10) y
| _ _ := 1
#eval f 1 1000
example (x y) : f (x+1) (y+1) = f (x+10) y :=
rfl
example (y) : f 0 (y+1) = 1 :=
rfl
example (x) : f (x+1) 0 = 1 :=
rfl
example : f 0 0 = 1 :=
rfl
|
91fef22a7fb78c7f6836831901593d099ef337b9 | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/algebra/ring/pi.lean | e4992ee2dcaadc46a4df1e3213384f909add6e34 | [
"Apache-2.0"
] | permissive | ayush1801/mathlib | 78949b9f789f488148142221606bf15c02b960d2 | ce164e28f262acbb3de6281b3b03660a9f744e3c | refs/heads/master | 1,692,886,907,941 | 1,635,270,866,000 | 1,635,270,866,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,329 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Patrick Massot
-/
import tactic.pi_instances
import algebra.group.pi
import algebra.ring.basic
/-!
# Pi instances for ring
This file defines instances for ring, semiring an... |
2dfd1d3d65761fffb1161d9bd10359e4b8b7ee5c | bdb33f8b7ea65f7705fc342a178508e2722eb851 | /algebra/ordered_ring.lean | 1189bbf49848d130ea0a32fa84ac850008fa84e1 | [
"Apache-2.0"
] | permissive | rwbarton/mathlib | 939ae09bf8d6eb1331fc2f7e067d39567e10e33d | c13c5ea701bb1eec057e0a242d9f480a079105e9 | refs/heads/master | 1,584,015,335,862 | 1,524,142,167,000 | 1,524,142,167,000 | 130,614,171 | 0 | 0 | Apache-2.0 | 1,548,902,667,000 | 1,524,437,371,000 | Lean | UTF-8 | Lean | false | false | 8,230 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import order.basic algebra.order algebra.ordered_group algebra.ring
universe u
variable {α : Type u}
-- TODO: this is necessary additionally to mul_nonneg otherwise... |
f97a6a74f86a20c5547ee996a5e94601f0eff831 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/algebra/group_power/basic.lean | 8a34317358e2f0b4a599752399d244bbb672b85e | [
"Apache-2.0"
] | permissive | abentkamp/mathlib | d9a75d291ec09f4637b0f30cc3880ffb07549ee5 | 5360e476391508e092b5a1e5210bd0ed22dc0755 | refs/heads/master | 1,682,382,954,948 | 1,622,106,077,000 | 1,622,106,077,000 | 149,285,665 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 19,575 | lean | /-
Copyright (c) 2015 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Robert Y. Lewis
-/
import algebra.ordered_ring
import tactic.monotonicity.basic
import deprecated.group
import group_theory.group_action.defs
/-!
# Power operations on m... |
759fa76a20d46f2419f1461072f3c286ea3e74ea | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/topology/support.lean | e52a6225b803984806e6379de6ec6eec60cc15a9 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 12,136 | lean | /-
Copyright (c) 2022 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Patrick Massot
-/
import topology.separation
/-!
# The topological support of a function
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file re... |
08c82015fc4ebfc678627f5ce27049a927912142 | 7b89826c26634aa18c0110f1634f73027851edfe | /natural-number-game/src/world02/level01.lean | 64182eb8baeb53c315377b428d2a743f81fdbd12 | [
"MIT"
] | permissive | marcofavorito/leanings | b7642344d8c9012a1cec74a804c5884297880c4d | 581b83be66ff4f8dd946fb6a1bb045d2ddf91076 | refs/heads/master | 1,672,310,991,244 | 1,603,031,766,000 | 1,603,031,766,000 | 279,163,004 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 289 | lean | import mynat.definition -- Imports the natural numbers.
import mynat.add -- imports addition.
namespace mynat -- hide
lemma zero_add (n : mynat) : 0 + n = n :=
begin [nat_num_game]
induction n with d hd,
rw add_zero,
refl,
rw add_succ,
rw hd,
refl,
end
end mynat -- hide
|
5e81a3e4ea38bac833d1eaf7802af82ab8b71ae9 | 7f15a2b0775be8a2fcb4936c6b0f127f683c4666 | /library/init/meta/interactive.lean | 8458ee409077171ee17054605925502880f0fad6 | [
"Apache-2.0"
] | permissive | mwillsey/lean | 0b90b5016a3158490d7c9cf8b836e8fe7bb3df81 | 8621be63353b299b0da9106f4e7c8ca5e271941d | refs/heads/master | 1,630,587,469,685 | 1,514,924,859,000 | 1,514,925,180,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 64,163 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.meta.tactic init.meta.rewrite_tactic init.meta.simp_tactic
import init.meta.smt.congruence_closure init.category.combinators
import init... |
6e1a2a568eb5cc7544e123724eac3312104e6213 | 2a70b774d16dbdf5a533432ee0ebab6838df0948 | /_target/deps/mathlib/src/ring_theory/jacobson.lean | 2f4c2d2aee91a50dd4ef99fe032e2579ed517d09 | [
"Apache-2.0"
] | permissive | hjvromen/lewis | 40b035973df7c77ebf927afab7878c76d05ff758 | 105b675f73630f028ad5d890897a51b3c1146fb0 | refs/heads/master | 1,677,944,636,343 | 1,676,555,301,000 | 1,676,555,301,000 | 327,553,599 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 21,893 | lean | /-
Copyright (c) 2020 Devon Tuma. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Devon Tuma
-/
import data.mv_polynomial
import ring_theory.ideal.over
import ring_theory.jacobson_ideal
import ring_theory.localization
/-!
# Jacobson Rings
The following conditions are ... |
5a7e52f7763aa999d689b68c1db3d40eed745136 | 947b78d97130d56365ae2ec264df196ce769371a | /stage0/src/Lean/Elab/Frontend.lean | d5b8779816c84572b722dfc4520212d2c8833e7f | [
"Apache-2.0"
] | permissive | shyamalschandra/lean4 | 27044812be8698f0c79147615b1d5090b9f4b037 | 6e7a883b21eaf62831e8111b251dc9b18f40e604 | refs/heads/master | 1,671,417,126,371 | 1,601,859,995,000 | 1,601,860,020,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,786 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Sebastian Ullrich
-/
import Lean.Elab.Import
import Lean.Elab.Command
namespace Lean
namespace Elab
namespace Frontend
structure Context :=
(commandStateRef... |
b5186026264878c26e798d8a868bf9a50ad17365 | 82b86ba2ae0d5aed0f01f49c46db5afec0eb2bd7 | /stage0/src/Lean/Data/Lsp/TextSync.lean | b1c910b97e668ed8c5c87dd481a20158c7b2f7f9 | [
"Apache-2.0"
] | permissive | banksonian/lean4 | 3a2e6b0f1eb63aa56ff95b8d07b2f851072d54dc | 78da6b3aa2840693eea354a41e89fc5b212a5011 | refs/heads/master | 1,673,703,624,165 | 1,605,123,551,000 | 1,605,123,551,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,627 | lean | /-
Copyright (c) 2020 Marc Huisinga. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Marc Huisinga, Wojciech Nawrocki
-/
import Lean.Data.Json
import Lean.Data.Lsp.Basic
/-! Section "Text Document Synchronization" of the LSP spec. -/
namespace Lean
namespace Lsp
ope... |
dc9fa8b2cdc58a7c14ae3bdb65aec9da038e048c | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/def12.lean | 9d8300b8408566c423a24cc44189a4c43d06d949 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 1,075 | lean | def diag : Bool → Bool → Bool → Nat
| b, true, false => 1
| false, b, true => 2
| true, false, b => 3
| b1, b2, b3 => default
theorem diag1 (a : Bool) : diag a true false = 1 :=
match a with
| true => rfl
| false => rfl
theorem diag2 (a : Bool) : diag false a true = 2 :=
by cases a; exact rfl; exact rfl
theorem ... |
3b1b0b1b82f43568a9a62d94a0bc82191b7e95fa | fe25de614feb5587799621c41487aaee0d083b08 | /src/Lean/Parser/Basic.lean | 6f9faef7c69d297975eab9b5abd38d5b07e5a0c7 | [
"Apache-2.0"
] | permissive | pollend/lean4 | e8469c2f5fb8779b773618c3267883cf21fb9fac | c913886938c4b3b83238a3f99673c6c5a9cec270 | refs/heads/master | 1,687,973,251,481 | 1,628,039,739,000 | 1,628,039,739,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 76,108 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Sebastian Ullrich
-/
/-!
# Basic Lean parser infrastructure
The Lean parser was developed with the following primary goals in mind:
* flexibility: Lean's g... |
0926c09ef4d3aebe35155d626344d1bde76dd89a | 4950bf76e5ae40ba9f8491647d0b6f228ddce173 | /src/category_theory/limits/shapes/binary_products.lean | b85dd18fd4a5398c106bf76baf20f47478a8af05 | [
"Apache-2.0"
] | permissive | ntzwq/mathlib | ca50b21079b0a7c6781c34b62199a396dd00cee2 | 36eec1a98f22df82eaccd354a758ef8576af2a7f | refs/heads/master | 1,675,193,391,478 | 1,607,822,996,000 | 1,607,822,996,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 32,795 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Bhavik Mehta
-/
import category_theory.limits.limits
import category_theory.limits.shapes.terminal
import category_theory.discrete_category
import category_theory.epi_m... |
ec40c59b316a035329d306d742ae78e1997e4e3d | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/topology/metric_space/hausdorff_distance.lean | 2b44116772422abef2b17ecac0fc0df336144b9f | [
"Apache-2.0"
] | permissive | Lix0120/mathlib | 0020745240315ed0e517cbf32e738d8f9811dd80 | e14c37827456fc6707f31b4d1d16f1f3a3205e91 | refs/heads/master | 1,673,102,855,024 | 1,604,151,044,000 | 1,604,151,044,000 | 308,930,245 | 0 | 0 | Apache-2.0 | 1,604,164,710,000 | 1,604,163,547,000 | null | UTF-8 | Lean | false | false | 33,604 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Sébastien Gouëzel
-/
import topology.metric_space.isometry
import topology.instances.ennreal
/-!
# Hausdorff distance
The Hausdorff distance on subsets of a metric (or emetric) spa... |
23dcc6a97394924795c5eaf793842c270722c3f9 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /library/data/real/basic.lean | 26845cbe12772e94294c5218b0d638e3a50d143b | [
"Apache-2.0"
] | permissive | soonhokong/lean-osx | 4a954262c780e404c1369d6c06516161d07fcb40 | 3670278342d2f4faa49d95b46d86642d7875b47c | refs/heads/master | 1,611,410,334,552 | 1,474,425,686,000 | 1,474,425,686,000 | 12,043,103 | 5 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 42,546 | lean | /-
Copyright (c) 2015 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Robert Y. Lewis
The real numbers, constructed as equivalence classes of Cauchy sequences of rationals.
This construction follows Bishop and Bridges (1985).
The construction of the rea... |
f20fe7c7beeea8a6a5374af14f400b826f36db68 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/utf8英語.lean | 1f655d71d5643664477f3f738b572616f041d508 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 475 | lean | def check_eq {α} [BEq α] [Repr α] (tag : String) (expected actual : α) : IO Unit :=
unless (expected == actual) do
throw $ IO.userError $
s!"assertion failure \"{tag}\":\n expected: {repr expected}\n actual: {repr actual}"
def DecodeUTF8: IO Unit := do
let cs := String.toList "Hello, 英語!"
let ns :=... |
78bd58d00ab1a56e81fa632655631257f4ed00aa | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /tests/lean/deprecated.lean | 97faa83124a66a6083057d908c0b1d855d6bb21a | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | EdAyers/lean4 | 57ac632d6b0789cb91fab2170e8c9e40441221bd | 37ba0df5841bde51dbc2329da81ac23d4f6a4de4 | refs/heads/master | 1,676,463,245,298 | 1,660,619,433,000 | 1,660,619,433,000 | 183,433,437 | 1 | 0 | Apache-2.0 | 1,657,612,672,000 | 1,556,196,574,000 | Lean | UTF-8 | Lean | false | false | 371 | lean | def g (x : Nat) := x + 1
@[deprecated g]
def f (x : Nat) := x + 1
@[deprecated]
def h (x : Nat) := x + 1
#eval f 0 + 1
#eval h 0
@[deprecated g1]
def f1 (x : Nat) := x + 1
def Foo.g1 := 10
@[deprecated Foo.g1]
def f2 (x : Nat) := x + 1
@[deprecated g1]
def f3 (x : Nat) := x + 1
open Foo
@[deprecated g1]
def f4... |
ef4f44ed720124a121848e82fcbb2418cff982f6 | 9d2e3d5a2e2342a283affd97eead310c3b528a24 | /src/hints/thursday/afternoon/category_theory/exercise2/hint3.lean | ac13c4ca35dca957d9d2c7c7aad727ca6d57c952 | [] | permissive | Vtec234/lftcm2020 | ad2610ab614beefe44acc5622bb4a7fff9a5ea46 | bbbd4c8162f8c2ef602300ab8fdeca231886375d | refs/heads/master | 1,668,808,098,623 | 1,594,989,081,000 | 1,594,990,079,000 | 280,423,039 | 0 | 0 | MIT | 1,594,990,209,000 | 1,594,990,209,000 | null | UTF-8 | Lean | false | false | 2,065 | lean | import algebra.category.CommRing.basic
import data.polynomial
noncomputable theory -- the default implementation of polynomials is noncomputable
local attribute [irreducible] polynomial.eval₂
def Ring.polynomial : Ring ⥤ Ring :=
{ obj := λ R, Ring.of (polynomial R),
map :=
begin
-- The goal is `Π {X Y : Ring... |
a51246a928d342380d98d77e0dec48d517e0dd29 | 6fbf10071e62af7238f2de8f9aa83d55d8763907 | /answers/hw5-exam1-practice-key.lean | abdb8eb1f9450bc147fdadbff8b402e2b3449b81 | [] | no_license | HasanMukati/uva-cs-dm-s19 | ee5aad4568a3ca330c2738ed579c30e1308b03b0 | 3e7177682acdb56a2d16914e0344c10335583dcf | refs/heads/master | 1,596,946,213,130 | 1,568,221,949,000 | 1,568,221,949,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,916 | lean | /-
Grading rubric. 7 points per question up to 100 max.
Partial credit by subproblem.
-/
/-
Note: An incorrect answer above or below
a correct answer can cause Lean to be unable
to process the correct answer. If you are not
able to complete a problem succesfully please
comment out your incomplete answer so that we
can... |
1e6fb2840f2425d6f6f0a6dc8885eff326af666e | 1e3a43e8ba59c6fe1c66775b6e833e721eaf1675 | /src/ring_theory/algebra.lean | 22514df16f4cef1d119cde0944dd5fc36ea597ee | [
"Apache-2.0"
] | permissive | Sterrs/mathlib | ea6910847b8dfd18500486de9ab0ee35704a3f52 | d9327e433804004aa1dc65091bbe0de1e5a08c5e | refs/heads/master | 1,650,769,884,257 | 1,587,808,694,000 | 1,587,808,694,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 21,872 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Yury Kudryashov
-/
import data.complex.basic
import data.matrix.basic
import linear_algebra.tensor_product
import algebra.commute
/-!
# Algebra over Commutative Semiring (under ... |
51a29c0e3c9a87dd694646126caf98bc11ee6a02 | 75db7e3219bba2fbf41bf5b905f34fcb3c6ca3f2 | /tests/lean/check2.lean | 210449e6e372390310e9a4c61b885567975d8263 | [
"Apache-2.0"
] | permissive | jroesch/lean | 30ef0860fa905d35b9ad6f76de1a4f65c9af6871 | 3de4ec1a6ce9a960feb2a48eeea8b53246fa34f2 | refs/heads/master | 1,586,090,835,348 | 1,455,142,203,000 | 1,455,142,277,000 | 51,536,958 | 1 | 0 | null | 1,455,215,811,000 | 1,455,215,811,000 | null | UTF-8 | Lean | false | false | 30 | lean | import logic
check eq.rec_on
|
7372876c3bbf521be61247b98132033d6655c790 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/geometry/manifold/derivation_bundle.lean | 4b156516a99c890a39696b264c4e385f70a99c60 | [
"Apache-2.0"
] | permissive | robertylewis/mathlib | 3d16e3e6daf5ddde182473e03a1b601d2810952c | 1d13f5b932f5e40a8308e3840f96fc882fae01f0 | refs/heads/master | 1,651,379,945,369 | 1,644,276,960,000 | 1,644,276,960,000 | 98,875,504 | 0 | 0 | Apache-2.0 | 1,644,253,514,000 | 1,501,495,700,000 | Lean | UTF-8 | Lean | false | false | 6,350 | lean | /-
Copyright © 2020 Nicolò Cavalleri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicolò Cavalleri
-/
import geometry.manifold.algebra.smooth_functions
import ring_theory.derivation
/-!
# Derivation bundle
In this file we define the derivations at a point of a m... |
b874692a49b42eb6f3ee72d0d185ba478c520968 | f5f7e6fae601a5fe3cac7cc3ed353ed781d62419 | /src/topology/metric_space/hausdorff_distance.lean | 230e56bbc152a268f52b961b3b7c7b9e6127164c | [
"Apache-2.0"
] | permissive | EdAyers/mathlib | 9ecfb2f14bd6caad748b64c9c131befbff0fb4e0 | ca5d4c1f16f9c451cf7170b10105d0051db79e1b | refs/heads/master | 1,626,189,395,845 | 1,555,284,396,000 | 1,555,284,396,000 | 144,004,030 | 0 | 0 | Apache-2.0 | 1,533,727,664,000 | 1,533,727,663,000 | null | UTF-8 | Lean | false | false | 32,188 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Sébastien Gouëzel
The Hausdorff distance on subsets of a metric (or emetric) space.
Given two subsets `s` and `t` of a metric space, their Hausdorff distance is the smallest `d`
such... |
1e4cca8a6c49e75b0b0c2df327c2b661796b08eb | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/653.lean | da3249b7fe50e5e4bf1fe283130ba1e3059696d5 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 91 | lean | structure Color
(red : Nat) (green : Nat) (blue : Nat)
def yellow := Color.mk 255 255 0
|
d86513d55afe8973e89c5d2ebe11ee544c46f6f9 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/rebind_bind.lean | dad708e6a8275e98f0d8d61be8d4562aae08e57d | [
"Apache-2.0"
] | permissive | leanprover-community/lean | 12b87f69d92e614daea8bcc9d4de9a9ace089d0e | cce7990ea86a78bdb383e38ed7f9b5ba93c60ce0 | refs/heads/master | 1,687,508,156,644 | 1,684,951,104,000 | 1,684,951,104,000 | 169,960,991 | 457 | 107 | Apache-2.0 | 1,686,744,372,000 | 1,549,790,268,000 | C++ | UTF-8 | Lean | false | false | 290 | lean | class mono_monad (m : Type) (α : out_param Type) :=
(pure : α → m)
(bind : m → (α → m) → m)
export mono_monad (bind pure)
instance : mono_monad bool bool :=
{ pure := id, bind := λ b f, if b then f b else b }
#eval do b ← tt,
b' ← ff,
mono_monad.pure b
|
8c5fb70bba9745041adbe6034cf0dd5b7ecf281f | 4fa161becb8ce7378a709f5992a594764699e268 | /src/algebra/ordered_field.lean | 347c826d3d4f776605690210b0ffea6517e519f3 | [
"Apache-2.0"
] | permissive | laughinggas/mathlib | e4aa4565ae34e46e834434284cb26bd9d67bc373 | 86dcd5cda7a5017c8b3c8876c89a510a19d49aad | refs/heads/master | 1,669,496,232,688 | 1,592,831,995,000 | 1,592,831,995,000 | 274,155,979 | 0 | 0 | Apache-2.0 | 1,592,835,190,000 | 1,592,835,189,000 | null | UTF-8 | Lean | false | false | 25,409 | lean | /-
Copyright (c) 2014 Robert Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Lewis, Leonardo de Moura, Mario Carneiro
-/
import algebra.ordered_ring
import algebra.field
set_option default_priority 100 -- see Note [default priority]
set_option old_structu... |
ccfa51e93a5b3c9a9709b71e4f897d17fa66b51d | dd4e652c749fea9ac77e404005cb3470e5f75469 | /src/missing_mathlib/algebra/ring.lean | 1c0a0e01fee79ce58909f5ba822297daf7a3df18 | [] | no_license | skbaek/cvx | e32822ad5943541539966a37dee162b0a5495f55 | c50c790c9116f9fac8dfe742903a62bdd7292c15 | refs/heads/master | 1,623,803,010,339 | 1,618,058,958,000 | 1,618,058,958,000 | 176,293,135 | 3 | 2 | null | null | null | null | UTF-8 | Lean | false | false | 279 | lean | import algebra.ring
universes u v
variable {α : Type u}
section domain
variable [domain α]
lemma mul_ne_zero_iff {a b : α} : a * b ≠ 0 ↔ a ≠ 0 ∧ b ≠ 0 :=
by classical; rw [←not_iff_not, not_and_distrib, not_not, not_not, not_not, mul_eq_zero]
end domain |
68188943eb42dfc8f8700faf15f0a826ad94cd78 | d29d82a0af640c937e499f6be79fc552eae0aa13 | /src/data/multiset/basic.lean | f0a5749680b3f21c8fa86f9d6f93329dfa3c9a9c | [
"Apache-2.0"
] | permissive | AbdulMajeedkhurasani/mathlib | 835f8a5c5cf3075b250b3737172043ab4fa1edf6 | 79bc7323b164aebd000524ebafd198eb0e17f956 | refs/heads/master | 1,688,003,895,660 | 1,627,788,521,000 | 1,627,788,521,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 98,589 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import data.list.perm
/-!
# Multisets
These are implemented as the quotient of a list by permutations.
## Notation
We define the global infix notation `::ₘ` f... |
66d24d4fb459af5229be5e041ade158fa8ab0fb5 | 367134ba5a65885e863bdc4507601606690974c1 | /src/linear_algebra/affine_space/finite_dimensional.lean | 2be14bb1fe36bc72af1b5f740da217d839da20a7 | [
"Apache-2.0"
] | permissive | kodyvajjha/mathlib | 9bead00e90f68269a313f45f5561766cfd8d5cad | b98af5dd79e13a38d84438b850a2e8858ec21284 | refs/heads/master | 1,624,350,366,310 | 1,615,563,062,000 | 1,615,563,062,000 | 162,666,963 | 0 | 0 | Apache-2.0 | 1,545,367,651,000 | 1,545,367,651,000 | null | UTF-8 | Lean | false | false | 16,030 | lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Joseph Myers.
-/
import linear_algebra.affine_space.independent
import linear_algebra.finite_dimensional
/-!
# Finite-dimensional subspaces of affine spaces.
This file provides a few re... |
fbf2f39741e517cff0a6005a9c72e08ea4b66057 | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /tests/lean/K_bug.lean | b1299db12ce5e5e68ba97859a0f135d65eb3eca0 | [
"Apache-2.0"
] | permissive | davidmueller13/lean | 65a3ed141b4088cd0a268e4de80eb6778b21a0e9 | c626e2e3c6f3771e07c32e82ee5b9e030de5b050 | refs/heads/master | 1,611,278,313,401 | 1,444,021,177,000 | 1,444,021,177,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 379 | lean | open eq.ops
inductive Nat : Type :=
zero : Nat |
succ : Nat → Nat
namespace Nat
definition pred (n : Nat) := Nat.rec zero (fun m x, m) n
theorem pred_succ (n : Nat) : pred (succ n) = n := rfl
theorem succ.inj {n m : Nat} (H : succ n = succ m) : n = m
:= calc
n = pred (succ n) : pred_succ n⁻¹
... = pred (succ ... |
39dcffedf98e1767b26b8988371066477b870f42 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/analysis/normed_space/finite_dimension.lean | c0630ce511a04f6ab7a3de3ea5df8bedd1193029 | [
"Apache-2.0"
] | permissive | AntoineChambert-Loir/mathlib | 64aabb896129885f12296a799818061bc90da1ff | 07be904260ab6e36a5769680b6012f03a4727134 | refs/heads/master | 1,693,187,631,771 | 1,636,719,886,000 | 1,636,719,886,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 33,259 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import analysis.normed_space.affine_isometry
import analysis.normed_space.operator_norm
import analysis.asymptotics.asymptotic_equivalent
import linear_algebra.... |
dd34f99652873a8b4c43181236983ea228c4c42a | 4727251e0cd73359b15b664c3170e5d754078599 | /src/algebra/module/linear_map.lean | 9bcc8774fa23debdb6f98fbd9bfed8c6b2332735 | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 33,799 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nathaniel Thomas, Jeremy Avigad, Johannes Hölzl, Mario Carneiro, Anne Baanen,
Frédéric Dupuis, Heather Macbeth
-/
import algebra.hom.group
import algebra.hom.group_action
import algebra... |
a0811e6236d1b13dffa095942782b49a06437563 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/group_theory/submonoid/membership.lean | d25b78b2e4ce69d9c474ab2efc0cf88ac3ce0916 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 23,453 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau, Johan Commelin, Mario Carneiro, Kevin Buzzard,
Amelia Livingston, Yury Kudryashov
-/
import group_theory.submonoid.operations
import algebra.big_operators.ba... |
39ce932882ac6d002f6098992bbea23debda4955 | 3863d2564418bccb1859e057bf5a4ef240e75fd7 | /hott/types/pointed.hlean | ccb68c5daa0d5fa6ef82667b5b4145baae754fc3 | [
"Apache-2.0"
] | permissive | JacobGross/lean | 118bbb067ff4d4af48a266face2c7eb9868fa91c | eb26087df940c54337cb807b4bc6d345d1fc1085 | refs/heads/master | 1,582,735,011,532 | 1,462,557,826,000 | 1,462,557,826,000 | 46,451,196 | 0 | 0 | null | 1,462,557,826,000 | 1,447,885,161,000 | C++ | UTF-8 | Lean | false | false | 27,563 | hlean | /-
Copyright (c) 2014-2016 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer, Floris van Doorn
Ported from Coq HoTT
The basic definitions are in init.pointed
-/
import .equiv .nat.basic
open is_trunc eq prod sigma nat equiv option is_e... |
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